Theta lifting and Langlands functoriality

  • Atsushi Ichino

    Department of Mathematics, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto 606-8502, Japan
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We review various aspects of theta lifting and its role in studying Langlands functoriality. In particular, we discuss realizations of the Jacquet–Langlands correspondence and the Shimura–Waldspurger correspondence in terms of theta lifting and their arithmetic applications.